Mass flowmeter methods, apparatus, and computer program products using correlation-measure-based status determination

ABSTRACT

Motion signals representing motion of a conduit of a mass flowmeter are mode selective filtered to generate a plurality of mode selective filtered motion signals such that the plurality of mode selective filtered motion signals preferentially represent motion associated with a vibrational mode of the conduit. A plurality of time difference estimates is generated from the plurality of mode selective filtered motion signals. A correlation measure is generated from the plurality of time difference estimates. A status of the mass flowmeter system is determined from the generated correlation measure. In some embodiments, the correlation measure comprises an intercept parameter of a scaling function that relates the plurality of time difference estimates to a plurality of reference time differences representing motion of the conduit at a known mass flow. In other embodiments, the correlation measure comprises a correlation coefficient estimated from the plurality of time difference estimates. In still other embodiments, the correlation measure comprises an error of estimate. The mass flowmeter system status may be determined by determining a change in the correlation measure, and corrective action may then be taken if the determined change satisfies a predetermined criterion. The invention may be embodied as methods, apparatus and computer program products.

FIELD OF THE INVENTION

[0001] The present invention relates to mass flowmeters and relatedmethods and apparatus, and more particularly, to methods, apparatus andcomputer program products for determining status of a mass flowmetersystem.

BACKGROUND OF THE INVENTION

[0002] Many sensor applications involve the detection of mechanicalvibration or other motion. Examples of sensors that utilize such motiondetection include Coriolis mass flowmeters and vibrating tubedensitometers. These devices typically include a conduit or other vesselthat is periodically driven, i.e., vibrated. Properties such as massflow, density and the like associated with a material contained in theconduit or vessel may be determined by processing signals from motiontransducers positioned on the containment structure, as the vibrationalmodes of the vibrating material-filled system generally are affected bythe combined mass, stiffness and damping characteristics of thecontaining conduit or vessel structure and the material containedtherein.

[0003] A typical Coriolis mass flowmeter includes one or more conduitsthat are connected inline in a pipeline or other transport system andconvey material, e.g., fluids, slurries and the like, in the system.Each conduit may be viewed as having a set of natural vibrational modesincluding, for example, simple bending, torsional, radial and coupledmodes. In a typical Coriolis mass flow measurement application, aconduit is excited at resonance in one of its natural vibrational modesas a material flows through the conduit, and motion of the conduit ismeasured at points along the conduit. Excitation is typically providedby an actuator, e.g., an electromechanical device, such as a voicecoil-type driver, that perturbs the conduit in a periodic fashion.Exemplary Coriolis mass flowmeters are described in U.S. Pat. Nos.4,109,524 to Smith, 4,491,025 to Smith et al., and Re. 31,450 to Smith.

[0004] Unfortunately, the accuracy of conventional Coriolis massflowmeters may be compromised by nonlinearities and asymmetries in theconduit structure, motion arising from extraneous forces, such as forcesgenerated by pumps and compressors that are attached to the flowmeter,and motion arising from pressure forces exerted by the material flowingthrough the flowmeter conduit. The effects of these forces are commonlyreduced for by using flowmeter designs that are balanced to reduceeffects attributable to external vibration, and by using frequencydomain filters, e.g., bandpass filters designed to filter out componentsof the motion signals away from the excitation frequency. However,mechanical filtering approaches are often limited by mechanicalconsiderations, e.g., material limitations, mounting constraints, weightlimitations, size limitations and the like, and frequency domainfiltering may be ineffective at removing unwanted vibrationalcontributions near the excitation frequency.

SUMMARY OF THE INVENTION

[0005] According to embodiments of the invention, a method of operatinga mass flowmeter system including a material-containing conduit isprovided. A plurality of motion signals representing motion of theconduit are mode selective filtered to generate a plurality of modeselective filtered motion signals such that the plurality of modeselective filtered motion signals preferentially represent motionassociated with a vibrational mode of the conduit. A plurality of timedifference estimates is generated from the plurality of mode selectivefiltered motion signals. A correlation measure is generated from theplurality of time difference estimates. A status of the mass flowmetersystem is determined from the generated correlation measure.

[0006] The step of generating a correlation measure may includeestimating an intercept parameter of a scaling function that relates theplurality of time difference estimates to a plurality of reference timedifferences representing motion of the conduit at a known mass flow. Forexample, an augmented matrix including the plurality of reference timedifferences may be generated, and the plurality of time differenceestimates may be multiplied by a pseudoinverse of the augmented matrixto estimate the intercept parameter. Alternatively, the scaling functionmay be iteratively estimated, e.g., using a least mean square (LMS)estimation procedure.

[0007] According to other embodiments of the invention, a correlationcoefficient may be estimated from the plurality of time differenceestimates, and the mass flowmeter system status may be determined fromthe estimated correlation coefficient. According to still otherembodiments of the invention, an error of estimate from the plurality oftime difference estimates, and the mass flowmeter system status may bedetermined from the estimated error of estimate.

[0008] In still other embodiments of the invention, the mass flowmetersystem status may be determined by determining a change in thecorrelation measure. Corrective action may then be taken if thedetermined change satisfies a predetermined criterion. For example, amode selective filter used to generate the mode selective filteredmotion signals may be modified based on the determined status of themass flowmeter system. In other embodiments, a pseudoinverse matrix maybe generated from a plurality of reference time differences representingmotion of the conduit under a known perturbation. The plurality of timedifference estimates may be multiplied by the psuedoinverse matrix toestimate a scaling function that relates the plurality of timedifference estimates to the plurality of reference time differences. Thepseudoinverse matrix may be modified based on the determined status ofthe mass flowmeter system.

[0009] According to still other embodiments of the invention, the massflowmeter system includes a plurality of motion transducers operativelyassociated with the conduit. Determining a mass flowmeter system statusmay include determining a status of a motion transducer from thegenerated correlation measure.

[0010] In other embodiments of the invention, an apparatus comprises aconduit configured to contain a material. A plurality of motiontransducers is operatively associated with the conduit and produces aplurality of motion signals that represent motion of the conduit. Asignal processing circuit receives the plurality of motion signals, modeselective filters a plurality of motion signals to generate a pluralityof mode selective filtered motion signals such that the plurality ofmode selective filtered motion signals preferentially represent motionassociated with a vibrational mode of the conduit, generates a pluralityof time difference estimates from the plurality of mode selectivefiltered motion signals, generates a correlation measure from theplurality of time difference estimates, and determines a status of theapparatus from the generated correlation measure.

[0011] According to still other embodiments of the invention, a computerprogram product for determining status of a mass flowmeter systemincluding a material-containing conduit is provided. The computerprogram product includes a computer readable storage medium embodyingcomputer readable program code, the computer-readable program codecomprising computer-readable program code that mode selective filters aplurality of motion signals representing motion of the conduit togenerate a plurality of mode selective filtered motion signals such thatthe plurality of mode selective filtered motion signals preferentiallyrepresent motion associated with a vibrational mode of the conduit, thatgenerates a plurality of time difference estimates from the plurality ofmode selective filtered motion signals, that generates a correlationmeasure from the plurality of time difference estimates, and thatdetermines a status of the mass flowmeter system from the generatedcorrelation measure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012]FIG. 1 is a schematic diagram conceptually illustrating acurved-tube flow sensor structure.

[0013]FIG. 2 is a schematic diagram conceptually illustrating astraight-tube flow sensor structure.

[0014]FIG. 3 is a schematic diagram illustrating a mass flow estimatingapparatus according to embodiments of the invention.

[0015]FIG. 4 is a schematic diagram illustrating a signal processingcircuit according to other embodiments of the invention.

[0016]FIG. 5 is a schematic diagram illustrating a mass flow estimatingapparatus according to other embodiments of the invention.

[0017]FIG. 6 is a schematic diagram illustrating an apparatus forestimating mass flow and density according to embodiments of theinvention.

[0018]FIG. 7 is a schematic diagram illustrating an apparatus forgenerating phase estimates according to embodiments of the invention.

[0019]FIG. 8 is a schematic diagram illustrating an apparatus forgenerating phase estimates according to other embodiments of theinvention.

[0020]FIG. 9 is a schematic diagram illustrating an apparatus forgenerating time difference estimates according to embodiments of theinvention.

[0021]FIG. 10 is a flowchart illustrating operations for estimating massflow according to embodiments of the invention.

[0022]FIG. 11 is a flowchart illustrating operations for estimating massflow according to other embodiments of the invention.

[0023]FIGS. 12 and 13 are waveform diagrams illustrating mass flowestimation operations according to the invention.

[0024]FIG. 14 is a flowchart illustrating operations for iterativelyestimating a mass flow scaling vector according to embodiments of thepresent invention.

[0025]FIG. 15 is a flowchart illustrating operations for generatingphase estimates according to embodiments of the invention.

[0026]FIG. 16 is a flowchart illustrating operations for estimating massflow according to other embodiments of the invention.

[0027]FIG. 17 is a flowchart illustrating operations for generatingdifference estimates according to embodiments of the invention.

[0028]FIG. 18 is a flowchart illustrating operations for estimating massflow according to embodiments of the invention.

[0029]FIG. 19 is a flowchart illustrating operations for estimatingdensity according to embodiments of the invention.

[0030]FIGS. 20A, 20B and 21-27 are waveform diagrams illustratingexemplary effects of system changes according to aspects of theinvention.

[0031] FIGS. 28-30 are flowcharts illustrating operations for monitoringsystem status and compensating for system changes according toembodiments of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

[0032] The present invention now will be described more fullyhereinafter with reference to the accompanying drawings, in whichpreferred embodiments of the invention are shown. This invention may,however, be embodied in many different forms and should not be construedas limited to the embodiments set forth herein; rather, theseembodiments are provided so that this disclosure will be thorough andcomplete, and will fully convey the scope of the invention to thoseskilled in the art. Like numbers refer to like elements throughout. Aswill be appreciated by one of skill in the art, the present inventionmay be embodied as systems (apparatus), methods, or computer programproducts.

[0033] The embodiments of the present invention described herein relateto Coriolis mass flowmeters. Those skilled in the art will appreciate,however, that the invention described herein is generally applicable todetermination of motion in a wide variety of mechanical structures, andthus the apparatus and methods of the present invention are not limitedto Coriolis mass flowmetering.

[0034] As will be appreciated by one of skill in the art, the presentinvention may be embodied as apparatus and/or method and/or computerprogram product. Accordingly, the present invention may be implementedin hardware or in a combination of hardware and software aspects.Furthermore, the present invention may also take the form of a computerprogram product including a computer-usable storage medium havingcomputer-usable program code embodied in the medium. Any suitablecomputer readable medium may be utilized, including semiconductor memorydevices (e.g., RAMs, ROMs, EEPROMs, and the like), hard disks, CD-ROMs,optical storage devices, and magnetic storage devices.

[0035] Computer program code for carrying out operations of the presentinvention may be written in an object oriented programming language,such as Java® or C++, and/or in a procedural programming languages, suchas “C.” The program code may execute one a single computer or dataprocessing device, such as a microcontroller, microprocessor, or digitalsignal processor (DSP), or may be executed on multiple devices, forexample, on multiple data processing devices that communicate via serialor parallel data busses within an electronic circuit board, chassis orassembly, or which form part of a data communications network such as alocal area network (LAN), wide area network (WAN), or internet.

[0036] The present invention is described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program code (instructions). These computer program code may beprovided to a processor of a general purpose computer, special purposecomputer, or other programmable data processing apparatus to produce amachine, such that the instructions, which execute via the processor ofthe computer or other programmable data processing apparatus, createmeans for implementing the functions specified in the flowchart and/orblock diagram block or blocks.

[0037] These computer program products also may be embodied in acomputer-readable storage medium (e.g., magnetic disk or semiconductormemory, code magnetic memory or the like) that can direct a computer orother programmable data processing apparatus to function in a particularmanner, such that the computer program stored in the computer-readablememory produce an article of manufacture including instruction meanswhich implement the function specified in the flowchart and/or blockdiagram block or blocks.

[0038] The computer program code may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that the codethat executes on the computer or other programmable apparatus providessteps for implementing the functions specified in the flowchart and/orblock diagram block or blocks.

[0039] Modal Behavior of a Vibrating Conduit

[0040] Behavior of a vibrating structure such as a Coriolis massflowmeter conduit may be described in terms of one or more natural modeshaving associated natural frequencies of vibration. The modes and theassociated natural frequencies may be mathematically described byeigenvectors and associated eigenvalues, the eigenvectors being uniquein relative magnitude but not absolute magnitude and orthogonal withrespect to the mass and stiffness of the structure. The linearlyindependent set of vectors may be used as a transformation to uncoupleequations that describe the structure's motion. In particular, theresponse of the structure to an excitation can be represented as asuperposition of scaled modes, the scaling representing the contributionof each mode to the motion of the structure. Depending on theexcitation, some modes may contribute more than others. Some modes maybe undesirable because they may contribute energy at the resonantfrequency of desired modes and, therefore, may corrupt measurementstaken at the resonant frequency of a desired mode, such as phasedifference measurements taken at the drive frequency.

[0041] Conventional Coriolis mass flowmeters typically use structuraland temporal filtering to reduce the effects of undesirable modes.Conventional structural filtering techniques include using mechanicalfeatures such as brace bars designed to decouple in phase and out ofphase bending modes, actuators positioned such that they are less likelyto excite undesirable modes, and transducers positioned such that theyare less sensitive to undesirable modes. Structural filtering techniquescan be very effective in reducing energy of undesired modes, but may belimited by geometric and fabrication constraints.

[0042] Temporal filtering techniques typically modify transducer signalsbased on time domain or frequency domain parameters. For example, atypical Coriolis mass flowmeter may include frequency domain filtersdesigned to remove frequency components that are significantlycorrelated with undesired modes. However, off-resonance energy fromundesired modes may contribute considerably to energy at the resonantfrequency of a desired mode. Because frequency-domain filters generallyare ineffective at distinguishing the contribution of multiple modes ata given frequency, the contribution of undesired modes at a measurementfrequency may be a significant source of error in process parametermeasurements.

[0043] A sensor conduit structure with negligible damping and zero flowmay be assumed to have purely real natural or normal modes of vibration,i.e., in each mode, each point of the structure reaches maximumdifference simultaneously. However, a real conduit having non-negligibledamping and a material flowing therethrough has a generally complexresponse to excitation, i.e., points of the structure generally do notsimultaneously reach maximum amplitude. The motion of the conduitstructure may be described as a complex mode having real and imaginarycomponents or, alternatively, magnitude and phase components. Coriolisforces imparted by the flowing material render motion of the sensorconduit mathematically complex.

[0044] Even if complex, motion of a conduit structure can be describedas a superposition of scaled natural (“normal” or “single degree offreedom” (SDOF)) modes, as the real and imaginary parts of a complexmode are linearly independent by definition. To represent complexmotion, complex scaling coefficients may be used in combining theconstituent real normal modes. Particular real normal modes may beclosely correlated with the imaginary component of the complex modewhile being significantly less correlated with the real component of thecomplex mode. Accordingly, these particular real normal modes may bemore closely correlated with the Coriolis forces associated with thematerial in the sensor conduit, and thus can provide information forgenerating an accurate estimate of a parameter associated with thematerial.

[0045] A conceptual model of one type of Coriolis mass flowmeter sensor100 is provided in FIG. 1. Motion transducers 105A, 105B, 105C, 105D(e.g., velocity transducers) are positioned to detect relative motion offirst and second curved conduits 103A, 103B of the sensor 100 that arevibrated by a an actuator 106 as a material 108 flows through theconduits 103A, 103B, the motion transducers 105A, 105B, 105C, 105Dproducing motion signals 109. A “straight tube” Coriolis flowmetersensor 200 illustrated in FIG. 2 includes a conduit 203 configured tocontain a material 208 from a pipeline 207 connected to the sensor 200at flanges 202. Within a housing 204 surrounding the conduit 203, anactuator 206 is operative to excite the conduit 203. Motion transducers205A, 205B, 205C, 205D (e.g., velocity transducers, accelerometers orother motion-sensing devices) are positioned along the conduit 203. Themotion transducers 205A, 205B, 205C, 205D produce motion signals 209representing motion of the conduit 203 in response to a plurality offorces F that may include, for example, a drive force imparted by theactuator 206, Coriolis forces arising from the flowing material 208,pressure forces exerted by the material 208, and other extraneous forcessuch as forces imparted by the pipeline 207 and forces generated bypumps, compressors and other equipment (not shown) connected to thepipeline 207 and conveyed to the conduit 203 via the flanges 202.

[0046] For a flowmeter structure such as those illustrated in FIGS. 1and 2, a response vector x can be constructed from the signals producedby motion transducers that are operatively associated with thestructure, such as the motion signals 109, 209 produced by motiontransducers 105A, 105B, 105C, 105D, 205A, 205B, 205C, 205D of FIGS. 1and 2. For example, the motion signals may be sampled to generate motionsignal values x₁, x₂, . . . , x_(n) of a response vector x. A realnormal modal matrix Φ, that is, an eigenvector matrix relating thephysical motion vector to a modal motion vector η representing motion ina plurality of natural (SDOF) modes, may then be identified such that:

x={dot over (O)}

.   (1)

[0047] The modal matrix Φ can be identified using a number oftechniques. For example, trial and error or inverse techniques may beused as described in U.S. patent application Ser. No. 08/890,785, filedJul. 11, 1997, assigned to the assignee of the present application andincorporated by reference herein in its entirety.

[0048] Exemplary Mass Flowmeters

[0049] According to embodiments of the present invention, selectivemodal filtering techniques are used to produce mode selective filteredmotion signals that are then used to generate phase estimates, which arein turn used to generate a mass flow estimate. Exemplary embodimentsaccording to this aspect of the present invention will now be described,in particular, embodiments using “straight tube” sensors such as thesensor 200 of FIG. 2. Those skilled in the art will appreciate, however,that the present invention is also applicable to curved-conduitstructures, such as that used in the sensor 100 illustrated in FIG. 1,as well as to other material-containing structures used in massflowmeters, densitometers and the like. Those skilled in the art willfurther appreciate that the present invention is also applicable to thecharacterization of motion in a variety of other structures.

[0050]FIG. 3 illustrates a mass flow estimating apparatus 300 accordingto embodiments of the present invention. The apparatus 300 includes amaterial-containing conduit 203 and operatively associated motiontransducers 205A, 205B, 205C, 205D of a flowmeter sensor 200, along witha signal processing circuit 301 that is operative to generate a massflow estimate from motion signals 305 produced by the motion transducers205A, 205B, 205C, 205D. Like numbers are used in FIGS. 2 and 3 to denotelike components of the sensor 200, detailed description of which willnot be repeated here in light of the description of FIG. 2.

[0051] The signal processing circuit 301 includes a mode selectivefilter 310 that is configured to receive the motion signals 305 andoperative to selectively pass one or more components of the motionsignals 305 to produce a plurality of mode selective filtered motionsignals 315. The mode selective filter 310 is preferably derived from amodal characterization of the sensor 200 as described in U.S. patentapplication Ser. No. 09/116,410, filed Jul. 16, 1998 (Attorney DocketNo. 7003/029), the disclosure of which is incorporated by referenceherein in its entirety. The signal processing circuit 301 also includesa phase estimator 320 that is responsive to the mode selective filteredmotion signals 315 and operative to generate a plurality of phaseestimates 325 therefrom. The signal processing circuit 301 furtherincludes a mass flow estimator 330 that is responsive to the phaseestimator 320 and produces a mass flow estimate 335 from the pluralityof phase estimates 325.

[0052]FIG. 4 illustrates an exemplary implementation of a mode selectivefilter 410, phase estimator 420 and mass flow estimator 430 according toembodiments of the present invention. A plurality of motion signals 405a, e.g., analog outputs from velocity or other motion transducersoperatively associated with a conduit or other material-containingvessel, is sampled and digitized by an A/D converter 440, producing aplurality of digital motion signals 405 b. The digital motion signals405 b are processed by a digital mode selective filter 410 to produce aplurality of mode selective filtered digital motion signals 415. Adigital phase estimator 420 generates a plurality of digital phaseestimates 425 from the plurality of mode selective filtered digitalmotion signals 415. A digital mass flow estimator 430 produces a digitalmass flow estimate 435 from the plurality of digital phase estimates425. As shown, the mode selective filter 410, the phase estimator 420and the mass flow estimator 430 may be implemented as computer readableprogram code executed by a data processor 450, for example, acombination of a computer (e.g., a microcontroller, microprocessor,digital signal processor (DSP), or other computing device) and anassociated storage medium (e.g., semiconductor memory magnetic storageand/or optical storage).

[0053]FIG. 5 illustrates an exemplary mass flow estimating apparatus 500according to other embodiments of the present invention. The apparatus500 includes a material-containing conduit 203 and operativelyassociated motion transducers 205A, 205B, 205C, 205D of a straight-tubesensor 200 such as that described with reference to FIG. 2, furtherdetailed description of which will not be repeated in light of thedescription of FIG. 2. A signal processing circuit 501 includes a modeselective filter 510 that is configured to receive the motion signals505 produced by the sensor 200 and operative to selectively pass one ormore components of the motion signals 505 to produce a plurality of modeselective filtered motion signals 515. The mode selective filter 510 isfurther operative to produce at least one modal motion signal 517, i.e.,at least one signal that represents motion of the conduit 203 in a modaldomain defined by at least one natural (SDOF) mode of the conduit 203.The mode selective filter 510 is preferably derived from a modalcharacterization of the sensor 200 as described in the aforementionedU.S. patent application Ser. No. 09/116,410, filed Jul. 16, 1998(Attorney Docket No. 7003/029).

[0054] The signal processing circuit 501 further includes a phaseestimator 520 that is responsive to the mode selective filter 510 andoperative to generate a plurality of phase estimates 525 from theplurality of mode selective filtered motion signals 515. The signalprocessing circuit 501 also includes a mass flow estimator 530 that isresponsive to the phase estimator 520 and produces a mass flow estimate535 from the plurality of phase estimates 525 using at least one modefrequency estimate 545 generated by a mode frequency estimator 540. Themode frequency estimator 540 produces the at least one mode frequencyestimate 545 responsive to the at least one modal motion signal 517. Thesignal processing circuit 501 further includes a density estimator 550that is responsive to the at least one mode frequency estimate 545 togenerate a density estimate 555.

[0055]FIG. 6 illustrates an apparatus 600 operative to estimate massflow and density from a plurality of motion signals 605, according toembodiments of the invention. The apparatus 600 includes a modeselective filter 610, a phase estimator 620, a mass flow estimator 630,a mode frequency estimator 640 and a density estimator 650. The modeselective (or “mode pass”) filter 610 includes a modal transformation612 that transforms a plurality of motion signals 605 into a pluralityof modal motion signals 613 that represent motion in a plurality ofnatural modes, as described above with reference to equation (1) and inthe aforementioned U.S. patent application Ser. No. 09/116,410, filedJul. 16, 1998 (Attorney Docket No. 7003/029). The mode selective filter610 also includes a mode selective transformation 614 that selectivelytransforms the plurality of modal motion signals 613 back out of themodal domain, producing mode selective filtered motion signals 615 thatare filtered such that components of the original motion signals 615that are associated with one or more desired modes are preferentiallypassed in relation to components associated with other, undesirednatural modes. Such a mode selective transformation is also described inU.S. patent application Ser. No. 09/116,410, filed Jul. 16, 1998(Attorney Docket No.7003/029). The modal motion signals 613 are passedon to the mode frequency estimator 640, which generates one or more modefrequency estimates 645.

[0056] The mode selective filtered motion signals 615 are passed on tothe phase estimator 620, which generates a plurality of phase estimates625 therefrom using a phase reference that is derived from the pluralityof motion signals 605. For example, as described in detail withreference to FIG. 7 below, the phase reference may be derived from oneor more of the mode selective filtered motion signals 615.Alternatively, the phase reference may be derived from one or more modefrequency estimates 645 generated from one or more of the modal motionsignals 613 by the mode frequency estimator 640.

[0057] The phase estimates 625 are passed onto the mass flow estimator630 that includes a time difference estimator 632 and a spatialintegrator 634. Using the one or more mode frequency estimates 645generated by the mode frequency estimator 640, the time differenceestimator 632 generates a plurality of time difference estimates 633from the plurality of phase estimates 625. The time difference estimator640 may also use zero-flow reference time differences 631, i.e., valuesrepresenting time differences under a zero mass flow condition which maycorrupt measurements at other mass flow rates, to generate timedifferences 633 that are corrected for such “zero offset.” As describedbelow, an estimate of a drive mode frequency may be generated by themode frequency estimator 640, and phase estimates may be divided by thisestimated drive mode frequency to yield uncorrected time differenceestimates. The uncorrected time difference estimates may then becorrected using the zero-flow reference time differences 631 (e.g., bysubtraction therefrom) to generate the time difference estimates 633.

[0058] The time difference estimates 633 generated by the timedifference estimator 632 are provided to a spatial integrator 634. Asdescribed in detail below, the spatial integrator 634 may determine aslope parameter of a scaling vector function that relates the pluralityof time difference estimates 633 to a plurality reference timedifferences 637 corresponding to a known mass flow. This slope parametermay then be used to generate a mass flow estimate 635 from the knownmass flow.

[0059] As also shown in FIG. 6, the density estimator 650 may also usethe mode frequency estimate 645 to generate an estimate of density ofthe material for which mass flow is being determined. The densityestimator 650 may utilize techniques similar to those used to generate adensity estimate 655 from a non-mode selective filtered transducersignal, such as those described in U.S. Pat. No. 5,687,100 to Buttler etal (issued Nov. 11, 1997) and U.S. Pat. No. 5,295,084 to Arunachalam etal. (issued Mar. 15, 1994), incorporated by reference herein in theirentireties. For example, according to embodiments of the presentinvention, density estimates may be generated by using modal frequencyestimates in place of the conventional frequency estimates utilized inthe aforementioned patents.

[0060] FIGS. 7-9 illustrate exemplary structures for implementingvarious components of FIG. 6. It will be appreciated that the modeselective filter 610, phase estimator 620, mass flow estimator 630, themode frequency estimator 640 of FIG. 6, as well as the structures ofFIGS. 7-9, may be implemented in a digital domain, e.g., as executablemodules, subroutines, objects and/or other types of software and/orfirmware running on a microprocessor, microcontroller, DSP or othercomputing device. In such implementations, “signals,” such as the modalmotion signals 613, mode selective filtered motion signals 615 and phaseestimates 633 may include vectors of digital signal values that areproduced at calculation intervals and upon which computations areperformed to implement the functions described. However, it will beappreciated that all or some of these signals may, in general, bedigital or analog, and that the operations performed thereon may beperformed by special-purpose digital hardware and/or analogous analoghardware.

[0061]FIG. 7 illustrates an example of a phase estimator 700 accordingto embodiments of the present invention. The phase estimator 700includes a frequency estimator 710 that estimates a frequency of a modeselective filtered motion signal 701, of a plurality of mode selectivefiltered motion signals 701 ₁, 701 ₂, . . . 701 _(n). The frequencyestimator 710 produces a frequency estimate 715 which is applied to aquadrature reference signal generator 720 that generates first andsecond (e.g., sine and cosine) reference signals 725 a, 725 b that havethe estimated frequency and that are in phase quadrature with respect toone another. The frequency estimator 710 may, for example, be adigitally-implemented adaptive notch filter that is operative todetermine the frequency estimate 715, and the quadrature referencesignal generator 720 may generate the quadrature reference signals 725a, 725 b using a “twiddle” function, in a manner similar to thatdescribed in U.S. patent application Ser. No. 09/344,840 (AttorneyDocket No. 5010 071/P98024) entitled Multi-Rate Digital Signal Processorfor Signals from Pick-Offs on a Vibrating Conduit, filed Jun. 28, 1999,assigned to the assignee of the present invention, and incorporatedherein by reference in its entirety. However, it will be appreciatedthat other techniques, including other digital and analog signalprocessing techniques for generating phase and quadrature referencesignals, may be used to generate the frequency estimate 715 and/or thequadrature reference signals 725 a, 725 b. For example, rather thangenerating the frequency estimate 715 from a mode-selectively filteredsignal as shown in FIG. 7, the frequency estimate may be a modefrequency estimate, such as one or more of the mode frequency estimates645 produced by the mode frequency estimator 640 of FIG. 6.

[0062] The first and second phase reference signals 725 a, 725 b areapplied to a plurality of phase calculators 730 ₁, 730 ₂, . . . , 730_(n), respective ones of which generate respective phase estimates 735₁, 735 ₂, . . . , 735 _(n) from respective ones of the mode selectivefiltered motion signals 701 ₁, 701 ₂, . . . , 701 _(n). Phase estimates735 ₂, . . . , 735 _(n) are then normalized with respect to one of thephase estimates phase estimates 735 ₁ by a normalizer 740 to produce aplurality of normalized phase estimates 745 ₁, 745 ₂, . . . , 745 _(n).The normalized phase estimates 745 ₁, 745 ₂, . . . , 745 _(n) may thenbe used to estimate mass flow, as described above with reference to FIG.6.

[0063] Referring again to FIG. 6, the mode frequency estimator 640 mayuse frequency estimation techniques similar to those described abovewith reference to FIG. 7. For example, the frequency-determiningadaptive notch filtering techniques described in the aforementioned U.S.patent application Ser. No. 09/344,840 (Attorney Docket No. 5010071/P98024) entitled Multi-Rate Digital Signal Processor for Signalsfrom Pick-Offs on a Vibrating Conduit may be used to generate at leastone frequency estimate 645 for at least one of the modal motion signals617.

[0064] Exemplary computing operations for demodulating a mode selectivefiltered motion signal 701 j using the synthesized quadrature (e.g.,sine and cosine) reference signals 725 a, 725 b are illustrated in FIG.8. The mode selective filtered motion signal 701 j is separatelymultiplied by each of the quadrature reference signals 725 a, 725 b,generating real and imaginary component signals 805 b, 805 a. Anarctangent calculator 810 then computes an arctangent of the real andimaginary component signals 805 b, 805 a to generate a phase estimate735 j. Preferably, the real and imaginary component signals 805 b, 805 aare filtered before application to the arctangent calculator 810, suchthat non-DC components of the signals 805 b, 805 a are attenuated.

[0065]FIG. 9 illustrates an exemplary computing structure for generatingcorrected time difference estimates 633 according to embodiments of thepresent invention. A vector of phase estimates 625 (which may benormalized) is divided by an estimated mode frequency 645, preferablyone or more frequencies associated with a drive mode. The resultingvector of time differences 915 is then corrected by subtracting acorresponding vector of zero-flow reference time differences 631,producing a vector of corrected time difference estimates 633. A similarcorrection could alternatively be achieved by subtracting a vector ofphase values associated with zero flow from the phase estimates 735 ₁,735 _(n), . . . , 735 _(n) described above.

[0066] Spatial Integration of Time Difference Estimates

[0067] According to other aspects of the present invention, timedifferences estimates, such as the corrected time difference estimatesdescribed above, may be processed using a “spatial integration”procedure to produce a mass flow estimate. According to variousembodiments of the present invention described below, numeroustechniques may be used to determine a slope parameter that relates timedifference estimates associated with an unknown mass flow to referencetime differences associated with a known mass flow, includingclosed-form pseudoinverse techniques and iterative techniques. Thisslope parameter may be used to generate an estimate of the unknown massflow.

[0068] As described in the aforementioned U.S. patent application Ser.No. 09/116,410, filed Jul. 16, 1998 (Attorney Docket No. 7003/029), avector Y_(e) of time difference values at known mass flow F_(c) may beidentified, and an unknown mass flow can be described in terms of thisreference time difference vector Y_(e) by a scalar multiplication, thatis, a vector of estimated time differences X_(e) for an unknown massflow can be scaled by a scale factor a (hereinafter referred to as a“slope parameter”) to produce the reference time difference vectorY_(e). In order to determine the unknown mass flow, the known mass flowF_(c) is multiplied by the slope parameter a. The reference timedifference vector Y_(e) and the time difference estimate vector X_(e)may be related as: $\begin{matrix}{X_{e} = {{aY}_{e} + {b{{\begin{matrix}{RU} \\{SV} \\{TW}\end{matrix}}.}}}} & (2)\end{matrix}$

[0069] Rearranging equation (2) gives: $\begin{matrix}{{X_{e} = {{\begin{bmatrix}\quad & 1 \\Y_{e} & \vdots \\\quad & 1\end{bmatrix}\begin{Bmatrix}a \\b\end{Bmatrix}} = {Zc}}},} & (3)\end{matrix}$

[0070] where the augmented matrix Z is formed by augmenting thereference time difference vector Y_(e) with a column of ones. Equation(3) may be solved for the scaling vector c by premultiplying the timedifference estimate vector X_(e) by the pseudo inverse W of theaugmented matrix Z:

c=Z⁻¹X_(e)=WX_(e),   (4)

[0071] where the matrix inverse operator (⁻¹) is used to denote a pseudoinverse. Solving for the vector c and then multiplying F_(c) by theslope parameter a of the vector c can yield an estimate of mass flow.

[0072]FIGS. 10 and 11 are flowchart illustrations of exemplaryoperations for generating a mass flow estimate from a plurality of timedifference estimates according to various embodiments of the presentinvention. Those skilled in the art will understand that the operationsof these flowchart illustrations may be can be implemented usingcomputer instructions. These instructions may be executed on a computeror other data processing apparatus, such as the data processor 450 ofFIG. 4, to create an apparatus (system) operative to perform theillustrated operations. The computer instructions may also be stored ascomputer readable program code on a computer readable medium, forexample, an integrated circuit memory, a magnetic disk, a tape or thelike, that can direct a computer or other data processing apparatus toperform the illustrated operations, thus providing means for performingthe illustrated operations. The computer readable program code may alsobe executed on a computer or other data-processing apparatus to causethe apparatus to perform a computer-implemented process. Accordingly,FIGS. 10 and 11 support apparatus (systems), computer program productsand methods for performing the operations illustrated therein.

[0073]FIG. 10 illustrates operations 1000 for generating a mass flowestimate from a vector X_(e) of time difference estimates along theabove-described lines according to embodiments of the present invention.A pseudoinverse W of an augmented matrix Z including a vector ofreference time differences Y_(e) associated with a known mass flow F_(c)augmented by a column of bones is determined (Block 1010). Thedetermination of the augmented matrix Z and the pseudoinverse matrix Wmay be done on an intermittent basis, e.g., at calibration, to reducecomputational burdens. The vector of time difference estimates X_(e) ismultiplied by the pseudoinverse matrix W, to produce a scaling vector c,including a slope parameter a and an intercept parameter b (Block 1020).The slope parameter a is then multiplied by the known mass flow F_(c) toproduce a mass flow estimate (Block 1030). It will be appreciated thatthe mass flow estimate may be further processed; for example, the massflow estimate may be averaged with other mass flow estimates determinedover a time period to produce a filtered mass flow measurement (Block1040). The intercept parameter b may also be monitored, for example, todetect system changes (Block 1050).

[0074] There are several advantages to monitoring the interceptparameter b of the vector c, as will be discussed in detail below.However, it is not necessary to calculate the intercept parameter b inorder to generate a mass flow estimate. Equation (2) can be rewrittenas:

X_(e)=Y_(e)a   (5)

[0075] using no intercept parameter b. Equation (5) may be viewed as anattempt to match the shape of the time difference estimate vector X_(e)to the shape of the reference time difference vector Y_(e) withoutaccounting for phase normalization. Equation (5) may work if the timedifference estimate vector Y_(e) and the reference time differencevector X_(e) are arbitrarily normalized, and may produce better resultsif all of the phases are normalized by the reference phase beforedetermination of the time difference estimates X_(e). To solve for theslope parameter a, the following relation may be used:

a=Y_(e) ⁻X_(e).   (6)

[0076]FIG. 11 illustrates operations 1100 for generating a mass flowestimate without determining the intercept parameter b according toembodiments of the present invention. A pseudoinverse Y_(e) ⁻¹ of vectorof reference time differences Y_(e) associated with a known mass flowF_(c) is determined (Block 1110). The determination of the pseudoinverseY_(e) ⁻¹ may be done on an intermittent basis, e.g., at calibration, toreduce computational burdens. The vector of time difference estimatesX_(e) is multiplied by the pseudoinverse Y_(e) ⁻¹ to determine a slopeparameter a (Block 1120). The slope parameter a is then multiplied bythe known mass flow F_(c) to produce a mass flow estimate (Block 1130).It will be appreciated that the mass flow estimate may be furtherprocessed; for example, the mass flow estimate may be averaged withother mass flow estimates determined over a time period to produce afiltered mass flow measurement (Block 1140).

[0077]FIGS. 12 and 13 graphically illustrate test results for aprototype Coriolis mass flowmeter according to embodiments of theinvention that indicate that determination of the intercept parameter bis not needed to generate mass flow estimates. In particular, FIGS. 12and 13 illustrates that mass flow estimates generated over timeintervals of interest (approximately 10 to approximately 30 seconds)using respective ones of the pseudoinverse methods described above(i.e., with and without determination of the intercept parameter b,respectively) show a similar degree of agreement with experimental massflow rate measurements for the time intervals obtained using othermeans.

[0078] According to other embodiments of the present invention, aiterative technique may be used to solve for the vector c in place ofthe pseudoinverse techniques described above. An error equation

L(k)=X _(e)(k)−Zc(k−1),   (7)

[0079] and an associated cost function $\begin{matrix}{J = {\frac{1}{2}L^{2}}} & (8)\end{matrix}$

[0080] can be defined. A gradient method can be used to find a solutionthat reduces the cost function J to a desired level, with the gradientgiven by: $\begin{matrix}{\frac{\partial J}{\partial c} = {- {{LZ}.}}} & (9)\end{matrix}$

[0081] Small steps may be taken down the gradient towards a minimumvalue of the cost function J. At a kth step, a new estimate of thevector c(k) is produced using the following relation: $\begin{matrix}{{{c(k)} = {{{c\left( {k - 1} \right)} - {\gamma \quad \frac{\partial J}{\partial c}}} = {{c\left( {k - 1} \right)} + {\gamma \quad {LZ}}}}},} & (10)\end{matrix}$

[0082] where the vector c(k−1) represents the result produced by thepreceding k−1 iteration and γ is an adaptive rate for the process.Computations may be repeatedly performed until the cost function J isreduced to a predetermined level. γ should be greater than zero and lessthan 2 to ensure convergence. The value of γ generally impacts the rateof convergence and the sensitivity of the iterative process to noise.Generally, the larger the value of γ, the faster the process converges;however, a large value for γ may increase sensitivity to noise. Anoptimum value for γ may be determined experimentally, which a typicallyvalue being 0.1.

[0083] Equation (10) represents a Least Mean Square (LMS) approach toparameter estimation. A potentially more robust Normalized Least MeanSquare (NLMS) version of this adaptive approach may also be used asfollows: $\begin{matrix}{{{c(k)} = {{c\left( {k - 1} \right)} - {\gamma \quad \frac{Z^{T}{L(k)}}{\alpha + {Z}_{2}^{2}}}}},} & (11)\end{matrix}$

[0084] where

0<γ<2   (12),

[0085] and α is a constant that is included to reduce the likelihood ofnumerical instability if the norm of Z approaches zero. In order toprovide convergence for equation (11), equation (12) should besatisfied. The value of α preferably is a small positive value and maybe selected based on experimentation.

[0086]FIG. 14 illustrates operations 1400 according to embodiments ofthe present invention, in which a scaling vector c is iterativelydetermined along the lines described above. A vector X_(e) of timedifference estimates is generated (Block 1410). An initial scalingvector estimate c(k) is generated (Block 1420). The initial value c(k)may be, for example, zero or a final estimate of a scaling vector cgenerated from a previous value of X_(e). Assuming that flow rate doesnot change drastically between flow measurements, the latter choice mayincrease the speed of convergence, as the previously estimated value forthe scaling vector c should be close to the new value to be determined.An associated error L(k) and cost J(k) are determined, e.g., usingequations (7) and (8) (Block 1440). If the cost J(k) is less than apredetermined value, indicating an acceptable accuracy of the scalingvector estimate c(k), an estimate of mass flow may be generated (Blocks1450, 1455) and a new vector of time difference estimates X_(e)generated (Block 1410). If not, an updated estimate of the scalingvector c(k) is generated using, for example, equation (10) or equation(11) (Blocks 1460, 1470), and new error and cost function values arecomputed (Blocks 1430, 1440).

[0087] Those skilled in the art will appreciate that operations otherthan those described with reference to FIG. 14 may be used with thepresent invention. For example, it will be appreciated that many of thecomputations may be combined or varied. It will also be appreciated thatthere are many different iterative techniques that can be used to solveequation (3) beyond the LMS and NLMS techniques described above.

[0088] FIGS. 15-19 are flowchart illustrations of exemplary operationsaccording to various embodiments of the present invention. Those skilledin the art will understand that the operations of these flowchartillustrations may be implemented using computer instructions. Theseinstructions may be executed on a computer or other data processingapparatus, such as the data processor 450 of FIG. 4, to create anapparatus (system) operative to perform the illustrated operations. Thecomputer instructions may also be stored as computer readable programcode on a computer readable medium, for example, an integrated circuitmemory, a magnetic disk, a tape or the like, that can direct a computeror other data processing apparatus to perform the illustratedoperations, thus providing means for performing the illustratedoperations. The computer readable program code may also be executed on acomputer or other data-processing apparatus to cause the apparatus toperform a computer-implemented process. Accordingly, FIGS. 15-19 supportapparatus (systems), computer program products and methods forperforming the operations illustrated therein.

[0089] According to embodiments of the present invention illustrated byFIG. 15, operations 1500 for generating phase estimates associated withmotion of a structure include mode selective filtering a plurality ofmotion signals representing motion of the structure to generate acorresponding plurality of mode selective filtered motion signals using,for example, techniques such as those described above with reference toFIG. 6. (Block 1510). A plurality of phase estimates is then generatedfrom the plurality of mode selective filtered motion signals (Block1520).

[0090] In exemplary mass flow estimation operations 1600 according toembodiments of the present invention illustrated in FIG. 16, a pluralityof motion signals representing motion of a conduit are mode selectivefiltered to produce a plurality of mode selective filtered motionsignals (Block 1610). A plurality of phase estimates is then generatedfrom the plurality of mode selective filtered motion signals (Block1620), and is used to generate a mass flow estimate (Block 1630).

[0091] In exemplary difference estimation operations 1700 according toother embodiments of the present invention illustrated in FIG. 17, aplurality of motion signals representing motion of a structure are modeselective filtered to produce a plurality of mode selective filteredmotion signals (Block 1710). A frequency of a first mode selectivefiltered motion signal is determined using, for example, the adaptivenotch filtering operations described above with reference to FIG. 7(Block 1720). A difference estimate, e.g., a phase difference estimateand/or a time difference estimate, is then determined from a second modeselective filtered motion signal using, for example, the demodulationoperations described with reference to FIG. 7. (Block 1730).

[0092]FIG. 18 illustrates Operations 1800 for generating a mass flowestimate according to yet other embodiments of the present invention. Aplurality of motion signals representing motion of a conduit areprocessed to generate a plurality of difference estimates, for example,time difference estimates or phase difference estimates (Block 1810). Aslope parameter relating the plurality of difference estimates to aplurality of reference difference values corresponding to a known massflow is then estimated (Block 1820), and a mass flow estimate isgenerated from the estimated slope parameter and the known mass flow(Block 1830). These operations may be implemented using, for example,the operations described above with reference to FIGS. 10 and 11.

[0093] In exemplary density estimation operations 1900 according toother embodiments of the present invention illustrated in FIG. 19, amodal transformation is applied to a plurality of motion signalsrepresenting motion of a material-containing vessel to generate at leastone modal motion signal representing corresponding motion in a modaldomain defined by at least one vibrational mode of the vessel (Block1910). At least one mode frequency is then determined from the at leastone modal motion signal (Block 1920), and a density of the material inthe vessel is determined from the at least one mode frequency estimate(Block 1930), for example, as described above with reference to FIG. 6.

[0094] Monitoring of Spatial Intercept or Other Correlation Measures toDetect System Status

[0095] As mentioned above with reference to FIGS. 10 and 11, althoughthe intercept parameter b of the scaling vector c is not needed for massflow estimation, it may be useful for detecting system changes, such asmotion transducer failure, changes in mounting conditions and the like.Potential usefulness of the intercept parameter is illustrated by thegraphs of FIGS. 20A-20B and 21. FIGS. 20A-20B graphically illustratessimulated changes in computed mass flow rate and spatial interceptparameter, respectively, for failures of a motion transducer atapproximately 20 seconds, the failure of particular transducer beingsimulated by zeroing out the corresponding elements in the vectors oftime difference estimates produced by the transducer. As shown in FIG.20A, loss of a transducer produces a change in computed mass flow rate,which might be erroneously interpreted as an actual change in mass flowrate.

[0096] The change in the intercept parameter may be used, according toembodiments of the present invention, to trigger a fault correctionscheme. For example, as shown in FIGS. 20A and 20B, the pseudoinverse Wof an augmented matrix Z may be recalculated by striking the rowcorresponding to the failed transducer, and then used to generate newmass flow estimates. As shown in FIG. 20A, where such a correction isimplemented for mass flow estimates beginning at approximately 40seconds, improved accuracy may be achieved. In particular, for theexample shown, an error of 0.5% is achieved with such a correction incomparison to the 4% error occurring without such a correction.

[0097] As shown in FIG. 21, which illustrates intercept parameter valuesfor failures of each member of a group of five motion transducers,failures of a motion transducer may be signaled by a corresponding largechange in the intercept parameter, a phenomenon which typically wouldnot occur in response to a mere change in mass flow. Other systemchanges, such as changes in mounting or other conditions, may also beidentified by changes in the intercept parameter. In particular, FIG. 22illustrates changes in the intercept parameter for a prototype Coriolismass flow meter after damping is added to the structure of the meter.

[0098] The intercept parameter is one of a variety of differentcorrelation measures that may be used to detect system changes accordingto embodiments of the present invention. In general, once a scalingvector c has been calculated, equation (3) above can be applied to givea vector of time differences X_(est), which is a least square fit of a“measured” vector of time differences X_(e) ( produced as describedabove) to a basis vector:

X_(est)=Zc.   (13)

[0099] The predicted vector of time differences X_(est) may be comparedto the measured vector of time difference estimates X_(e) to produce acorrelation measure that can be used for various purposes. Thecomparison can be done intermittently or at each computation of massflow.

[0100] In embodiments of the present invention, a coefficient ofcorrelation r may generated from the predicted vector of timedifferences X_(est) and used to detect system changes. The coefficientof correlation r is a dimensionless scalar quantity between +1 and −1,and uses a quantity {overscore (X)}, which is an average of the timedifference estimates X_(e): $\begin{matrix}{{\overset{\_}{X} = {{{mean}\left( X_{e} \right)} = {\sum\limits_{i = 1}^{N}\frac{X_{ei}}{N}}}},} & (14)\end{matrix}$

[0101] where N is the number of data points, e.g., the number of motiontransducer signals. The correlation coefficient r may be defined as aratio of explained variation over total variation: $\begin{matrix}{r = {{\pm \sqrt{\frac{explainedvariation}{totalvariation}}} = {\pm {\sqrt{\frac{\sum\left( {X_{est} - \overset{\_}{X}} \right)^{2}}{\sum\left( {X_{e} - \overset{\_}{X}} \right)^{2}}}.}}}} & (15)\end{matrix}$

[0102]FIG. 23 illustrates how such a correlation coefficient may beused, in particular, in detecting transducer failure. Mass flow isestimated over a first time period of 0 to 15 seconds using vectorsX_(e) of time difference estimates generated from motion signalsproduced by transducers #1-#5. Subsequently produced vectors X_(e) oftime difference estimates are then perturbed by zeroing out motionsignal values corresponding to one motion transducer (#2) from 15 to 30seconds, simulating failure of that transducer for that time period.Vectors X_(e) of time difference estimates are again perturbed from 45to 60 seconds by doubling the motion signal value associated with the #2transducer, simulating a gain change in the transducer or a “noisy”transducer signal. As seen in FIG. 23, the mass flow estimate is reducedapproximately 20 lbm/min low when the #2 transducer input is zeroed andincreased approximately 15 lbm/min with the motion signal input doubled.

[0103] With standard flow measurement techniques, it may be difficult totell whether such changes are attributable to actual mass flow changesor measurement failures. However, in a manner similar to that describedabove with reference to the intercept parameter, the correlationcoefficient r may be used to detect such system changes. As shown inFIG. 24, which illustrates behavior of the correlation coefficient rover the same time interval as FIG. 23, the correlation coefficient rmay show a relatively large change in value with a failed (zeroed) ornoisy motion signal.

[0104] Error of estimate is another correlation measure that may be usedfor detecting system status. A standard error of estimate s_(x,y) may beexpressed as: $\begin{matrix}{s_{x,y} = \sqrt{\frac{\sum\left( {X_{e} - X_{est}} \right)^{2}}{N}}} & (16)\end{matrix}$

[0105] As shown in FIG. 25, which shows behavior of the standard errorof estimate s_(x,y) for the time interval of FIGS. 23 and 24, thestandard error of estimate s_(x,y) may exhibit large changes for thesystem changes described above (it will be noted that sampling theoryindicates that for a small number of transducer inputs (e.g., 6),greater accuracy may be achieved by replacing the N in the denominatorwith N−2.)

[0106] Other properties of the error of estimate measure can beexploited to determine the source of a failure, such as the identity ofa particular failed transducer. The standard error of estimate may beviewed as being analogous to the standard deviation of a data set, i.e.,one can expect that 99.7% of the time, the error of estimate for a timedifference estimate will be within three times the standard errorestimate s_(x,y) of the predicted vector of time differences X_(est).Accordingly, the respective errors of estimate for respective timedifference estimates associated with respective transducers can bechecked to see if they are within a predetermined multiple (e.g., withinthree times) of the standard error of the estimate. Such a test may beexpressed as the following inequality:

X _(est) −K*s _(x,y) ≦X _(e) ≦X _(est) +K*s _(x,y),   (17)

[0107] which can be rearranged to give:

−K*s _(x,y) ≦X _(e) −X _(est) ≦+K*s _(x,y)   (18).

[0108] To identify a failed transducer, for example, the criterion ofequations (17) and (18) can be applied to each component of eachgenerated vector of time difference estimates. An error (X_(e)−X_(est))of a particular time difference estimate X_(e) associated with a failedtransducer will typically be many times the standard error of estimate.This is illustrated in FIG. 26, which shows error (X_(e)−X_(est)) for afailed transducer #2 of a group of transducers in relation to thestandard error of estimate for the group (the values of which arenormalized for convenience by subtracting out a nominal vector). Asshown, the error associated with transducer #2 is well outside thestandard error of estimate bounds for the group (which, for the exampleshown, is approximately ±0.07, too small to be seen on the plot of FIG.26).

[0109] It is also possible to correct the computed mass flow rate for afailed transducer once it has been identified. For example, theaugmented matrix Z may be reformulated by deleting the row associatedwith the failed transducer. A new pseudoinverse matrix W may then beformed by inverting the reformulated augmented matrix Z. Mass flow ratemay then be estimated premultiplying a reduced dimension vector of timedifference estimates X_(e) in which the row associated with the failedtransducer by the new pseudoinverse matrix W is zeroed out. FIG. 27illustrates such correction of a mass flow rate estimate.

[0110] According to embodiments of the present invention, a flowmeterapparatus may monitor an intercept parameter, correlation coefficient,standard error of estimate or other correlation measure to detect systemstatus. For example, upon detection of a large change in the interceptparameter, a particular failed transducer may be identified and themodal selective filter and/or the pseudoinverse matrix used by theapparatus to generate difference estimates may be recomputed tocompensate for the failed transducer. Similarly, an error of a timedifference estimate associated with a particular transducers movingoutside of a range defined by a standard error of estimate may be usedto detect transducer failure, and thus trigger corrective action.

[0111]FIG. 28 illustrates operations 2800 for detecting system statusaccording to embodiments of the present invention. A plurality ofdifference estimates, e.g., a vector of time difference estimates X_(e)as described above, is generated (Block 2810). A correlation measure,such as an intercept parameter, a correlation coefficient or an error ofestimate is determined (Block 2820). System status is determined fromthe determined correlation measure (Block 2830).

[0112]FIG. 29 illustrates exemplary operations 2900 according to otherembodiments of the present invention. A vector of time differenceestimates X_(e) is generated (Block 2910). A correlation measure, suchas an intercept parameter, a correlation coefficient or an error ofestimate, is determined (Block 2920). If a change in the correlationmeasure meets a predetermined criterion, a failed transducer isidentified (Blocks 2930, 2940). After identifying the failed transducer,appropriate elements of the augmented matrix Z may be zeroed out, andthe pseudoinverse matrix W may be recomputed for use in subsequent massflow and other computations (Blocks 2950, 2960, 2910). In this manner,input from the failed transducer may be excluded from subsequent massflow estimates.

[0113] Other corrective action may be taken based on a correlationmeasure. For example, in exemplary operations 3000 according toembodiments of the present invention illustrated in FIG. 30, anintercept parameter is monitored (Block 3010) and, if a change in theintercept parameter meets a predetermined criterion, the apparatus mayrecompute the mode selective filter it uses in generating mass flowestimates (Blocks 3020, 3030). A variety of change criteria may be used,such as criteria based on maximum deviation of the intercept parameterfrom an initial value, average deviation of the intercept parameter overa predetermined time interval, and the like.

[0114] Those skilled in the art will appreciate that the presentinvention may be implemented a number of other ways than the embodimentsdescribed herein. For example, computations described herein may beimplemented as separate computations, or may be combined into one ormore computations that achieve equivalent results. The functionsdescribed herein may, in general, be implemented using digital and/oranalog signal processing techniques. Those skilled in the art will alsoappreciate that, although the present invention may be embodied withinan apparatus such as a Coriolis mass flowmeter, or as methods which maybe performed by such apparatus, the present invention may also beembodied in a apparatus configured to operate in association with aflowmeter or sensor apparatus, such as in process control apparatus. Itwill also be appreciated that the present invention may be embodied inan article of manufacture in the form of computer-readable instructionsor program code embodied in a computer readable storage medium such as amagnetic disk, integrated circuit memory device, magnetic tape, bubblememory or the like. Such computer program code may be executed by acomputer or other data processor and executed responsive to motionsignals supplied from motion transducers operatively associated with astructure, such as a conduit or other vessel.

[0115] In the drawings and specification, there have been disclosedtypical preferred embodiments of the invention and, although specificterms are employed, they are used in a generic and descriptive senseonly and not for purposes of limitation, the scope of the inventionbeing set forth in the following claims.

That which is claimed is:
 1. A method of operating a mass flowmetersystem including a material-containing conduit, the method comprisingthe steps of: mode selective filtering a plurality of motion signalsrepresenting motion of the conduit to generate a plurality of modeselective filtered motion signals such that the plurality of modeselective filtered motion signals preferentially represent motionassociated with a vibrational mode of the conduit; generating aplurality of time difference estimates from the plurality of modeselective filtered motion signals; and generating a correlation measurefrom the plurality of time difference estimates; and determining astatus of the mass flowmeter system from the generated correlationmeasure.
 2. A method according to claim 1, wherein said step ofgenerating a correlation measure comprises the step of estimating anintercept parameter of a scaling function that relates the plurality oftime difference estimates to a plurality of reference time differencesrepresenting motion of the conduit at a known mass flow.
 3. A methodaccording to claim 2, wherein said step of estimating an interceptparameter comprises the steps of: generating an augmented matrixincluding the plurality of reference time differences; and multiplyingthe plurality of time difference estimates by a pseudoinverse of theaugmented matrix to estimate the intercept parameter.
 4. A methodaccording to claim 2, wherein said step of estimating an interceptparameter comprises the step of iteratively estimating the scalingfunction.
 5. A method according to claim 4, wherein said step ofiteratively estimating comprises the step of applying a least meansquare (LMS) estimation procedure.
 6. A method according to claim 2,wherein said step of estimating an intercept parameter is preceded bythe step of processing a plurality of motion signals representing motionof the conduit at the known mass flow to generate the plurality ofreference time differences.
 7. A method according to claim 1: whereinsaid step of generating a correlation measure comprises the step ofestimating a correlation coefficient from the plurality of timedifference estimates; and wherein said step of determining a massflowmeter system status comprises the step of determining the massflowmeter system status from the estimated correlation coefficient.
 8. Amethod according to claim 1: wherein said step of generating acorrelation measure comprises the step of estimating an error ofestimate from the plurality of time difference estimates; and whereinsaid step of determining a mass flowmeter system status comprises thestep of determining the mass flowmeter system status from the estimatederror of estimate.
 9. A method according to claim 1, wherein said stepof determining a mass flowmeter system status comprises the step ofdetermining a change in the correlation measure, and wherein the methodfurther comprises the step of taking corrective action if the determinedchange satisfies a predetermined criterion.
 10. A method according toclaim 1, wherein said step of mode selective filtering comprises thestep of applying a mode selective filter to the plurality of motionsignals, and wherein said step of taking corrective action comprises thestep of modifying the mode selective filter based on the determinedstatus of the mass flowmeter system.
 11. A method according to claim 1,further comprising the steps of: generating a pseudoinverse matrix froma plurality of reference time differences representing motion of theconduit under a known perturbation; and multiplying the plurality oftime difference estimates by the psuedoinverse matrix to estimate ascaling function that relates the plurality of time difference estimatesto the plurality of reference time differences; and modifying thepseudoinverse matrix based on the determined status of the massflowmeter system.
 12. A method according to claim 1, wherein the massflowmeter system includes a plurality of motion transducers operativelyassociated with the conduit, and wherein said step of mode selectivefiltering is preceded by the step of receiving the plurality of motionsignals from the plurality of motion transducers, and wherein said stepof determining a mass flowmeter system status comprises the step ofdetermining a status of a motion transducer from the generatedcorrelation measure.
 13. A method according to claim 12: wherein saidstep of generating a correlation measure comprises the steps of;determining a standard error of estimate from the plurality of timedifference estimates; and determining an error of estimate associatedwith a particular motion transducer; and wherein said step ofdetermining a status of a motion transducer comprises the step ofcomparing the error of estimate associate with the particular motiontransducer to the standard error of estimate.
 14. A method according toclaim 12: wherein said step of generating a correlation measurecomprises the step of estimating an intercept parameter of a scalingfunction that relates the plurality of time difference estimates to aplurality of reference time differences that represent motion of theconduit at a known mass flow; and wherein said step of determining astatus of a motion transducer comprises the step of comparing theestimated intercept parameter to a plurality of predetermined values toidentify a motion transducer.
 15. An apparatus, comprising: a conduitconfigured to contain a material; a plurality of motion transducers,operatively associated with the conduit, that produce a plurality ofmotion signals that represent motion of the conduit; a signal processingcircuit that receives the plurality of motion signals, mode selectivefilters a plurality of motion signals to generate a plurality of modeselective filtered motion signals such that the plurality of modeselective filtered motion signals preferentially represent motionassociated with a vibrational mode of the conduit, generates a pluralityof time difference estimates from the plurality of mode selectivefiltered motion signals, generates a correlation measure from theplurality of time difference estimates, and determines a status of theapparatus from the generated correlation measure.
 16. An apparatusaccording to claim 15, wherein the signal processing circuit estimatesan intercept parameter of a scaling function that relates the pluralityof time difference estimates to a plurality of reference timedifferences representing motion of the conduit at a known mass flow. 17.An apparatus according to claim 16, wherein the signal processingcircuit generates an augmented matrix including the plurality ofreference time differences and multiplies the plurality of timedifference estimates by a pseudoinverse of the augmented matrix toestimate the intercept parameter.
 18. An apparatus according to claim16, wherein the signal processing circuit iteratively estimates thescaling function.
 19. An apparatus according to claim 18, wherein thesignal processing circuit applies a least mean square (LMS) estimationprocedure.
 20. An apparatus according to claim 15, wherein the signalprocessing circuit estimates a correlation coefficient from theplurality of time difference estimates and determines the status fromthe estimated correlation coefficient.
 21. An apparatus according toclaim 15, wherein the signal processing circuit estimates an error ofestimate from the plurality of time difference estimates and determinesthe status from the estimated error of estimate.
 22. An apparatusaccording to claim 15, wherein the signal processing circuit determinesa status of a motion transducer from the generated correlation measure.23. A computer program product for determining status of a massflowmeter system including a material-containing conduit, the computerprogram product comprising: a computer readable storage medium embodyingcomputer readable program code, the computer-readable program codecomprising: first computer-readable program code that mode selectivefilters a plurality of motion signals representing motion of the conduitto generate a plurality of mode selective filtered motion signals suchthat the plurality of mode selective filtered motion signalspreferentially represent motion associated with a vibrational mode ofthe conduit, that generates a plurality of time difference estimatesfrom the plurality of mode selective filtered motion signals, thatgenerates a correlation measure from the plurality of time differenceestimates, and that determines a status of the mass flowmeter systemfrom the generated correlation measure.
 24. A computer program productaccording to claim 23, wherein the first computer readable program codeestimates an intercept parameter of a scaling function that relates theplurality of time difference estimates to a plurality of reference timedifferences representing motion of the conduit at a known mass flow, anddetermines the mass flowmeter system status from the estimated interceptparameter.
 25. A computer program product according to claim 23, whereinthe first computer program code estimates a correlation coefficient fromthe plurality of time difference estimates and determines the massflowmeter system status from the estimated correlation coefficient. 26.A computer program product according to claim 23, wherein the firstcomputer-readable program code estimates an error of estimate from theplurality of time difference estimates, and determines the massflowmeter system status from the estimated error of estimate.